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\begin{document}


\title{On-line Math 21}


\email{david.johnson@lehigh.edu}


\urladdr{http://www.lehigh.edu/\textasciitilde{}dlj0}

\maketitle

\section{The Zoo of functions}

The point of this chapter is to gather together all of the standard ``transcendental''
functions, dealing with their definitions, their properties, their derivatives
and integrals, and why they come up in calculus.


\subsection{Trigonometric functions (and their inverses)}

Trigonometric functions really come into their own in calculus. As a subject
of its own, trigonometry is often an overwhelming list of identities and definitions,
but in calculus, these functions model behavior that is essential for understanding
many natural phenomena, and quantify geometric relationships.


\subsection{Exponential and logarithmic functions}

Logarithms used to be primarily a calculational tool for dealing with complex
arithmetic computations. They formed the basis for the construction of slide
rules. But even though they are only of historical interest as a calculational
tool, they are still vital in calculus. These functions provide another great
source of models of natural processes, including many biological systems.


\subsection{Hyperbolic functions (and their inverses)}

Hyperbolic functions are often viewed as merely an arcane exercise in constructing
functions that look somewhat like trigonometric functions, but they do legitimately
model some physical and geometric phenomena, and are widely used in the sciences
and engineering. Since they are defined entirely in terms of exponential functions,
in a sense they are nothing new, but they do provide some new twists.

\end{document}
